{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "密度估计"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy.stats import norm\n",
    "from sklearn.neighbors import KernelDensity\n",
    "from sklearn.utils.fixes import parse_version\n",
    "\n",
    "# `normed` is being deprecated in favor of `density` in histograms\n",
    "if parse_version(matplotlib.__version__) >= parse_version('2.1'):\n",
    "    density_param = {'density': True}\n",
    "else:\n",
    "    density_param = {'normed': True}\n",
    "\n",
    "# ----------------------------------------------------------------------\n",
    "# Plot the progression of histograms to kernels\n",
    "np.random.seed(1)\n",
    "N = 20\n",
    "X = np.concatenate((np.random.normal(0, 1, int(0.3 * N)),\n",
    "                    np.random.normal(5, 1, int(0.7 * N))))[:, np.newaxis]\n",
    "X_plot = np.linspace(-5, 10, 1000)[:, np.newaxis]\n",
    "bins = np.linspace(-5, 10, 10)\n",
    "\n",
    "with plt.style.context('Solarize_Light2'):\n",
    "    fig, ax = plt.subplots(2, 2, sharex=True, sharey=True)\n",
    "    fig.subplots_adjust(hspace=0.05, wspace=0.05)\n",
    "\n",
    "    # histogram 1\n",
    "    ax[0, 0].hist(X[:, 0], bins=bins, **density_param)\n",
    "    ax[0, 0].text(-3.5, 0.31, \"Histogram\")\n",
    "\n",
    "    # histogram 2\n",
    "    ax[0, 1].hist(X[:, 0], bins=bins + 0.75, **density_param)\n",
    "    ax[0, 1].text(-3.5, 0.31, \"Histogram, bins shifted\")\n",
    "\n",
    "    # tophat KDE\n",
    "    kde = KernelDensity(kernel='tophat', bandwidth=0.75).fit(X)\n",
    "    log_dens = kde.score_samples(X_plot)\n",
    "    ax[1, 0].fill(X_plot[:, 0], np.exp(log_dens), )\n",
    "    ax[1, 0].text(-3.5, 0.31, \"Tophat Kernel Density\")\n",
    "\n",
    "    # Gaussian KDE\n",
    "    kde = KernelDensity(kernel='gaussian', bandwidth=0.75).fit(X)\n",
    "    log_dens = kde.score_samples(X_plot)\n",
    "    ax[1, 1].fill(X_plot[:, 0], np.exp(log_dens), )\n",
    "    ax[1, 1].text(-3.5, 0.31, \"Gaussian Kernel Density\")\n",
    "\n",
    "    for axi in ax.ravel():\n",
    "        axi.plot(X[:, 0], np.full(X.shape[0], -0.01), '+k')\n",
    "        axi.set_xlim(-4, 9)\n",
    "        axi.set_ylim(-0.02, 0.34)\n",
    "\n",
    "    for axi in ax[:, 0]:\n",
    "        axi.set_ylabel('Normalized Density')\n",
    "\n",
    "    for axi in ax[1, :]:\n",
    "        axi.set_xlabel('x')\n",
    "\n",
    "    plt.savefig('density-estimation-1.svg', transparent=True)\n",
    "\n",
    "# ----------------------------------------------------------------------\n",
    "# Plot all available kernels\n",
    "\n",
    "\n",
    "def format_func(x, loc):\n",
    "    if x == 0:\n",
    "        return '0'\n",
    "    elif x == 1:\n",
    "        return 'h'\n",
    "    elif x == -1:\n",
    "        return '-h'\n",
    "    else:\n",
    "        return '%ih' % x\n",
    "\n",
    "\n",
    "X_plot = np.linspace(-6, 6, 1000)[:, None]\n",
    "X_src = np.zeros((1, 1))\n",
    "\n",
    "with plt.style.context('Solarize_Light2'):\n",
    "\n",
    "    fig, ax = plt.subplots(2, 3, sharex=True, sharey=True)\n",
    "    fig.subplots_adjust(left=0.05, right=0.95, hspace=0.05, wspace=0.05)\n",
    "\n",
    "    for i, kernel in enumerate(['gaussian', 'tophat', 'epanechnikov', 'exponential', 'linear', 'cosine']):\n",
    "        axi = ax.ravel()[i]\n",
    "        log_dens = KernelDensity(kernel=kernel).fit(X_src).score_samples(X_plot)\n",
    "        axi.fill(X_plot[:, 0], np.exp(log_dens), '-k', )\n",
    "        axi.text(-2.6, 0.95, kernel)\n",
    "\n",
    "        axi.xaxis.set_major_formatter(plt.FuncFormatter(format_func))\n",
    "        axi.xaxis.set_major_locator(plt.MultipleLocator(1))\n",
    "        axi.yaxis.set_major_locator(plt.NullLocator())\n",
    "\n",
    "        axi.set_ylim(0, 1.05)\n",
    "        axi.set_xlim(-2.9, 2.9)\n",
    "\n",
    "    ax[0, 1].set_title('Available Kernels')\n",
    "\n",
    "    plt.savefig('density-estimation-2.svg', transparent=True)\n",
    "\n",
    "# ----------------------------------------------------------------------\n",
    "# Plot a 1D density example\n",
    "N = 100\n",
    "np.random.seed(1)\n",
    "X = np.concatenate((np.random.normal(0, 1, int(0.3 * N)),\n",
    "                    np.random.normal(5, 1, int(0.7 * N))))[:, np.newaxis]\n",
    "\n",
    "X_plot = np.linspace(-5, 10, 1000)[:, np.newaxis]\n",
    "\n",
    "true_dens = (0.3 * norm(0, 1).pdf(X_plot[:, 0])\n",
    "             + 0.7 * norm(5, 1).pdf(X_plot[:, 0]))\n",
    "\n",
    "with plt.style.context('Solarize_Light2'):\n",
    "\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.fill(X_plot[:, 0], true_dens, fc='black', alpha=0.2,\n",
    "            label='input distribution')\n",
    "    colors = ['navy', 'cornflowerblue', 'darkorange']\n",
    "    kernels = ['gaussian', 'tophat', 'epanechnikov']\n",
    "    lw = 2\n",
    "\n",
    "    for kernel in kernels:\n",
    "        kde = KernelDensity(kernel=kernel, bandwidth=0.5).fit(X)\n",
    "        log_dens = kde.score_samples(X_plot)\n",
    "        ax.plot(X_plot[:, 0], np.exp(log_dens), lw=lw,\n",
    "                linestyle='-', label=\"kernel = '{0}'\".format(kernel))\n",
    "\n",
    "    ax.text(6, 0.38, \"N={0} points\".format(N))\n",
    "\n",
    "    ax.legend(loc='upper left')\n",
    "    ax.plot(X[:, 0], -0.005 - 0.01 * np.random.random(X.shape[0]), '+k')\n",
    "\n",
    "    ax.set_xlim(-4, 9)\n",
    "    ax.set_ylim(-0.02, 0.4)\n",
    "\n",
    "    plt.savefig('density-estimation-3.svg', transparent=True)\n",
    "    \n",
    "plt.show()\n"
   ]
  }
 ],
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